Source code for openquake.hazardlib.calc.disagg

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
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"""
:mod:`openquake.hazardlib.calc.disagg` contains
:func:`disaggregation` as well as several aggregation functions for
extracting a specific PMF from the result of :func:`disaggregation`.
"""
import warnings
import operator
import collections
from functools import partial
import numpy
import scipy.stats

from openquake.baselib.general import AccumDict, groupby, pprod
from openquake.hazardlib.calc import filters
from openquake.hazardlib.geo.utils import get_longitudinal_extent
from openquake.hazardlib.geo.utils import (angular_distance, KM_TO_DEGREES,
                                           cross_idl)
from openquake.hazardlib.site import SiteCollection
from openquake.hazardlib.gsim.base import to_distribution_values
from openquake.hazardlib.contexts import (
    ContextMaker, get_probability_no_exceedance)

BIN_NAMES = 'mag', 'dist', 'lon', 'lat', 'eps', 'trt'
BinData = collections.namedtuple('BinData', 'dists, lons, lats, pnes')


[docs]def assert_same_shape(arrays): """ Raises an AssertionError if the shapes are not consistent """ shape = arrays[0].shape for arr in arrays[1:]: assert arr.shape == shape, (arr.shape, shape)
[docs]def get_edges_shapedic(oq, sitecol, mags_by_trt): """ :returns: (mag dist lon lat eps trt) edges and shape dictionary """ tl = oq.truncation_level if oq.rlz_index is None: Z = oq.num_rlzs_disagg or 1 else: Z = len(oq.rlz_index) # build mag_edges mags = set() trts = [] for trt, _mags in mags_by_trt.items(): mags.update(float(mag) for mag in _mags) trts.append(trt) mags = sorted(mags) mag_edges = oq.mag_bin_width * numpy.arange( int(numpy.floor(min(mags) / oq.mag_bin_width)), int(numpy.ceil(max(mags) / oq.mag_bin_width) + 1)) # build dist_edges maxdist = max(oq.maximum_distance.max().values()) dist_edges = oq.distance_bin_width * numpy.arange( 0, int(numpy.ceil(maxdist / oq.distance_bin_width) + 1)) # build eps_edges eps_edges = numpy.linspace(-tl, tl, oq.num_epsilon_bins + 1) # build lon_edges, lat_edges per sid lon_edges, lat_edges = {}, {} # by sid for site in sitecol: loc = site.location lon_edges[site.id], lat_edges[site.id] = lon_lat_bins( loc.x, loc.y, maxdist, oq.coordinate_bin_width) # sanity check: the shapes of the lon lat edges are consistent assert_same_shape(list(lon_edges.values())) assert_same_shape(list(lat_edges.values())) bin_edges = [mag_edges, dist_edges, lon_edges, lat_edges, eps_edges] edges = [mag_edges, dist_edges, lon_edges[0], lat_edges[0], eps_edges] shape = [len(edge) - 1 for edge in edges] + [len(trts)] shapedic = dict(zip(BIN_NAMES, shape)) shapedic['N'] = len(sitecol) shapedic['M'] = len(oq.imtls) shapedic['P'] = len(oq.poes_disagg or (None,)) shapedic['Z'] = Z return bin_edges + [trts], shapedic
def _eps3(truncation_level, n_epsilons): # NB: instantiating truncnorm is slow and calls the infamous "doccer" tn = scipy.stats.truncnorm(-truncation_level, truncation_level) eps = numpy.linspace(-truncation_level, truncation_level, n_epsilons + 1) eps_bands = tn.cdf(eps[1:]) - tn.cdf(eps[:-1]) return tn, eps, eps_bands DEBUG = AccumDict(accum=[]) # sid -> pnes.mean(), useful for debugging # this is inside an inner loop
[docs]def disaggregate(ctxs, tom, g_by_z, iml2dict, eps3, sid=0, bin_edges=()): """ :param ctxs: a list of U RuptureContexts :param tom: a temporal occurrence model :param g_by_z: an array of gsim indices :param iml2dict: a dictionary of arrays imt -> (P, Z) :param eps3: a triplet (truncnorm, epsilons, eps_bands) """ # disaggregate (separate) PoE in different contributions U, E, M = len(ctxs), len(eps3[2]), len(iml2dict) iml2 = next(iter(iml2dict.values())) P, Z = iml2.shape dists = numpy.zeros(U) lons = numpy.zeros(U) lats = numpy.zeros(U) # switch to logarithmic intensities iml3 = numpy.zeros((M, P, Z)) for m, (imt, iml2) in enumerate(iml2dict.items()): # 0 values are converted into -inf iml3[m] = to_distribution_values(iml2, imt) truncnorm, epsilons, eps_bands = eps3 cum_bands = numpy.array([eps_bands[e:].sum() for e in range(E)] + [0]) G = ctxs[0].mean_std.shape[1] mean_std = numpy.zeros((2, U, M, G), numpy.float32) for u, ctx in enumerate(ctxs): # search the index associated to the site ID; for instance # searchsorted([2, 4, 6], 4) => 1 idx = numpy.searchsorted(ctx.sids, sid) dists[u] = ctx.rrup[idx] # distance to the site lons[u] = ctx.clon[idx] # closest point of the rupture lon lats[u] = ctx.clat[idx] # closest point of the rupture lat for g in range(G): mean_std[:, u, :, g] = ctx.mean_std[:, g, :, idx] # (2, M) poes = numpy.zeros((U, E, M, P, Z)) pnes = numpy.ones((U, E, M, P, Z)) for (m, p, z), iml in numpy.ndenumerate(iml3): if iml == -numpy.inf: # zero hazard continue # discard the z contributions coming from wrong realizations: see # the test disagg/case_2 try: g = g_by_z[z] except KeyError: continue lvls = (iml - mean_std[0, :, m, g]) / mean_std[1, :, m, g] idxs = numpy.searchsorted(epsilons, lvls) poes[:, :, m, p, z] = _disagg_eps( truncnorm.sf(lvls), idxs, eps_bands, cum_bands) for u, ctx in enumerate(ctxs): pnes[u] *= get_probability_no_exceedance(ctx, poes[u], tom) # slow bindata = BinData(dists, lons, lats, pnes) DEBUG[idx].append(pnes.mean()) if not bin_edges: return bindata return _build_disagg_matrix(bindata, bin_edges)
[docs]def set_mean_std(ctxs, cmaker): for u, ctx in enumerate(ctxs): ctx.mean_std = cmaker.get_mean_stds([ctx])[:2]
def _disagg_eps(survival, bins, eps_bands, cum_bands): # disaggregate PoE of `iml` in different contributions, # each coming from ``epsilons`` distribution bins res = numpy.zeros((len(bins), len(eps_bands))) for e, eps_band in enumerate(eps_bands): res[bins <= e, e] = eps_band # left bins inside = bins == e + 1 # inside bins res[inside, e] = survival[inside] - cum_bands[bins[inside]] return res # shape (U, E) # used in calculators/disaggregation
[docs]def lon_lat_bins(lon, lat, size_km, coord_bin_width): """ Define lon, lat bin edges for disaggregation histograms. :param lon: longitude of the site :param lat: latitude of the site :param size_km: total size of the bins in km :param coord_bin_width: bin width in degrees :returns: two arrays lon bins, lat bins """ nbins = numpy.ceil(size_km * KM_TO_DEGREES / coord_bin_width) delta_lon = min(angular_distance(size_km, lat), 180) delta_lat = min(size_km * KM_TO_DEGREES, 90) EPS = .001 # avoid discarding the last edgebdata.pnes.shape lon_bins = lon + numpy.arange(-delta_lon, delta_lon + EPS, delta_lon / nbins) lat_bins = lat + numpy.arange(-delta_lat, delta_lat + EPS, delta_lat / nbins) if cross_idl(*lon_bins): lon_bins %= 360 return lon_bins, lat_bins
# this is fast def _build_disagg_matrix(bdata, bins): """ :param bdata: a dictionary of probabilities of no exceedence :param bins: bin edges :returns: a 7D-matrix of shape (#distbins, #lonbins, #latbins, #epsbins, M, P, Z) """ dist_bins, lon_bins, lat_bins, eps_bins = bins dim1, dim2, dim3, dim4 = shape = [len(b) - 1 for b in bins] # find bin indexes of rupture attributes; bins are assumed closed # on the lower bound, and open on the upper bound, that is [ ) # longitude values need an ad-hoc method to take into account # the 'international date line' issue # the 'minus 1' is needed because the digitize method returns the # index of the upper bound of the bin dists_idx = numpy.digitize(bdata.dists, dist_bins) - 1 lons_idx = _digitize_lons(bdata.lons, lon_bins) lats_idx = numpy.digitize(bdata.lats, lat_bins) - 1 # because of the way numpy.digitize works, values equal to the last bin # edge are associated to an index equal to len(bins) which is not a # valid index for the disaggregation matrix. Such values are assumed # to fall in the last bin dists_idx[dists_idx == dim1] = dim1 - 1 lons_idx[lons_idx == dim2] = dim2 - 1 lats_idx[lats_idx == dim3] = dim3 - 1 U, E, M, P, Z = bdata.pnes.shape mat7D = numpy.ones(shape + [M, P, Z]) for i_dist, i_lon, i_lat, pne in zip( dists_idx, lons_idx, lats_idx, bdata.pnes): mat7D[i_dist, i_lon, i_lat] *= pne # shape E, M, P, Z return 1. - mat7D def _digitize_lons(lons, lon_bins): """ Return indices of the bins to which each value in lons belongs. Takes into account the case in which longitude values cross the international date line. :parameter lons: An instance of `numpy.ndarray`. :parameter lons_bins: An instance of `numpy.ndarray`. """ if cross_idl(lon_bins[0], lon_bins[-1]): idx = numpy.zeros_like(lons, dtype=int) for i_lon in range(len(lon_bins) - 1): extents = get_longitudinal_extent(lons, lon_bins[i_lon + 1]) lon_idx = extents > 0 if i_lon != 0: extents = get_longitudinal_extent(lon_bins[i_lon], lons) lon_idx &= extents >= 0 idx[lon_idx] = i_lon return numpy.array(idx) else: return numpy.digitize(lons, lon_bins) - 1 def _magbin_groups(rups, mag_bins): # returns lists of ruptures, one list per each magnitude bin groups = [[] for _ in mag_bins[1:]] for rup in rups: magi = numpy.searchsorted(mag_bins, rup.mag) - 1 groups[magi].append(rup) return groups # this is used in the hazardlib tests, not in the engine
[docs]def disaggregation( sources, site, imt, iml, gsim_by_trt, truncation_level, n_epsilons, mag_bin_width, dist_bin_width, coord_bin_width, source_filter=filters.nofilter, **kwargs): """ Compute "Disaggregation" matrix representing conditional probability of an intensity mesaure type ``imt`` exceeding, at least once, an intensity measure level ``iml`` at a geographical location ``site``, given rupture scenarios classified in terms of: - rupture magnitude - Joyner-Boore distance from rupture surface to site - longitude and latitude of the surface projection of a rupture's point closest to ``site`` - epsilon: number of standard deviations by which an intensity measure level deviates from the median value predicted by a GSIM, given the rupture parameters - rupture tectonic region type In other words, the disaggregation matrix allows to compute the probability of each scenario with the specified properties (e.g., magnitude, or the magnitude and distance) to cause one or more exceedences of a given hazard level. For more detailed information about the disaggregation, see for instance "Disaggregation of Seismic Hazard", Paolo Bazzurro, C. Allin Cornell, Bulletin of the Seismological Society of America, Vol. 89, pp. 501-520, April 1999. :param sources: Seismic source model, as for :mod:`PSHA <openquake.hazardlib.calc.hazard_curve>` calculator it should be an iterator of seismic sources. :param site: :class:`~openquake.hazardlib.site.Site` of interest to calculate disaggregation matrix for. :param imt: Instance of :mod:`intensity measure type <openquake.hazardlib.imt>` class. :param iml: Intensity measure level. A float value in units of ``imt``. :param gsim_by_trt: Tectonic region type to GSIM objects mapping. :param truncation_level: Float, number of standard deviations for truncation of the intensity distribution. :param n_epsilons: Integer number of epsilon histogram bins in the result matrix. :param mag_bin_width: Magnitude discretization step, width of one magnitude histogram bin. :param dist_bin_width: Distance histogram discretization step, in km. :param coord_bin_width: Longitude and latitude histograms discretization step, in decimal degrees. :param source_filter: Optional source-site filter function. See :mod:`openquake.hazardlib.calc.filters`. :returns: A tuple of two items. First is itself a tuple of bin edges information for (in specified order) magnitude, distance, longitude, latitude, epsilon and tectonic region types. Second item is 6d-array representing the full disaggregation matrix. Dimensions are in the same order as bin edges in the first item of the result tuple. The matrix can be used directly by pmf-extractor functions. """ trts = sorted(set(src.tectonic_region_type for src in sources)) trt_num = dict((trt, i) for i, trt in enumerate(trts)) rlzs_by_gsim = {gsim_by_trt[trt]: [0] for trt in trts} by_trt = groupby(sources, operator.attrgetter('tectonic_region_type')) bdata = {} # by trt, magi sitecol = SiteCollection([site]) iml2 = numpy.array([[iml]]) eps3 = _eps3(truncation_level, n_epsilons) rups = AccumDict(accum=[]) cmaker = {} # trt -> cmaker for trt, srcs in by_trt.items(): tom = srcs[0].temporal_occurrence_model cmaker[trt] = ContextMaker( trt, rlzs_by_gsim, {'truncation_level': truncation_level, 'maximum_distance': source_filter.integration_distance(trt), 'imtls': {str(imt): [iml]}}) rups[trt].extend(cmaker[trt].from_srcs(srcs, sitecol)) min_mag = min(r.mag for rs in rups.values() for r in rs) max_mag = max(r.mag for rs in rups.values() for r in rs) mag_bins = mag_bin_width * numpy.arange( int(numpy.floor(min_mag / mag_bin_width)), int(numpy.ceil(max_mag / mag_bin_width) + 1)) for trt in cmaker: for magi, ctxs in enumerate(_magbin_groups(rups[trt], mag_bins)): set_mean_std(ctxs, cmaker[trt]) bdata[trt, magi] = disaggregate(ctxs, tom, [0], {imt: iml2}, eps3) if sum(len(bd.dists) for bd in bdata.values()) == 0: warnings.warn( 'No ruptures have contributed to the hazard at site %s' % site, RuntimeWarning) return None, None min_dist = min(bd.dists.min() for bd in bdata.values()) max_dist = max(bd.dists.max() for bd in bdata.values()) dist_bins = dist_bin_width * numpy.arange( int(numpy.floor(min_dist / dist_bin_width)), int(numpy.ceil(max_dist / dist_bin_width) + 1)) lon_bins, lat_bins = lon_lat_bins(site.location.x, site.location.y, max_dist, coord_bin_width) eps_bins = numpy.linspace(-truncation_level, truncation_level, n_epsilons + 1) bin_edges = (mag_bins, dist_bins, lon_bins, lat_bins, eps_bins) matrix = numpy.zeros((len(mag_bins) - 1, len(dist_bins) - 1, len(lon_bins) - 1, len(lat_bins) - 1, len(eps_bins) - 1, len(trts))) # 6D for trt, magi in bdata: mat7 = _build_disagg_matrix(bdata[trt, magi], bin_edges[1:]) matrix[magi, ..., trt_num[trt]] = mat7[..., 0, 0, 0] return bin_edges + (trts,), matrix
MAG, DIS, LON, LAT, EPS = 0, 1, 2, 3, 4 mag_pmf = partial(pprod, axis=(DIS, LON, LAT, EPS)) dist_pmf = partial(pprod, axis=(MAG, LON, LAT, EPS)) mag_dist_pmf = partial(pprod, axis=(LON, LAT, EPS)) mag_dist_eps_pmf = partial(pprod, axis=(LON, LAT)) lon_lat_pmf = partial(pprod, axis=(DIS, MAG, EPS)) mag_lon_lat_pmf = partial(pprod, axis=(DIS, EPS)) trt_pmf = partial(pprod, axis=(1, 2, 3, 4, 5)) # applied on matrix TRT MAG DIS LON LAT EPS
[docs]def lon_lat_trt_pmf(matrices): """ Fold full disaggregation matrices to lon / lat / TRT PMF. :param matrices: a matrix with T submatrices :returns: 4d array. First dimension represents longitude histogram bins, second one latitude histogram bins, third one trt histogram bins, last dimension is the z index, associatd to the realization. """ res = numpy.array([lon_lat_pmf(mat) for mat in matrices]) return res.transpose(1, 2, 0, 3)
# this dictionary is useful to extract a fixed set of # submatrices from the full disaggregation matrix pmf_map = dict([ ('Mag', mag_pmf), ('Dist', dist_pmf), ('TRT', trt_pmf), ('Mag_Dist', mag_dist_pmf), ('Mag_Dist_Eps', mag_dist_eps_pmf), ('Lon_Lat', lon_lat_pmf), ('Mag_Lon_Lat', mag_lon_lat_pmf), ('Lon_Lat_TRT', lon_lat_trt_pmf), ])